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ADAPTIVE CONTROL - DEFINITION ‘An adaptive controller is a controller with adjustable parameters and a mechanism for adjusting the parameters’ Department for Automatic Control and Electronics Department for Automatic Control and Electronics Faculty of Electrical Engineering Faculty of Electrical Engineering University of Sarajevo University of Sarajevo Sarajevo, December, 2013 Adnan Tahirovic

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Adaptive Control - General

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  • ADAPTIVE CONTROL - DEFINITION

    An adaptive controller is a controller with adjustable parameters and a mechanism for adjusting the parameters

    Department for Automatic Control and Electronics Department for Automatic Control and Electronics

    Faculty of Electrical EngineeringFaculty of Electrical Engineering

    University of SarajevoUniversity of SarajevoSarajevo, December, 2013

    Adnan Tahirovic

  • ADAPTIVE CONTROL - DEFINITION

  • ADAPTIVE CONTROL - HISTORY1960:

    State Space

    Stability Theory

    Stochastic Control Theory

    Dynamic Programming

    Common Framework for lerning and adaptive control theory

    System identification

    1970: 1970:

    Renaissance of adaptive control

    (different estination schemes combined with various design methods)

    1980:

    Stability of adaptive systems with strong assumptions

    Merging ideas of robust control and system identification

    Robustness of adaptive control

    Universal stability

    1990:

    Investigation of nonlinear systems

    Adaptive control strong relations with ideas on learning

  • AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS

    To design a robust controller, it is attempted to find acontroller such that the loop transfer function is large forthese frequencies at which there are large variations in theprocess transfer function.

  • AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS

  • AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS

  • AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS

  • AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS

  • AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS

    To judge the conseqences of process variations fromopen-loop dynamics, it is better to use frequency responsesthan time responses.

    It is necessary to have some information about thedesired crossover frequency of the closed-loop system.

  • AdCo HOW A LINEAR CONTROLLER CAN DEAL WITH VARIATIONS OF PROCESS DYNAMICS

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    MRAS solves a problem in which the performancespecifications are given in terms of a reference model.

    MRAS was originally introduced for flight control

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    MIT RULE:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    ALTERNATIVE:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    Adaptation of a feedforward gain:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    Adaptation of a feedforward gain:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    Adaptation of a feedforward gain:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    Adaptation of a feedforward gain:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    MRAS for a first order system:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    MRAS for a first order system:

    Perfect model following:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS)

    MRAS for a first order system:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS for a first order system:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS for a first order system:

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

    Barbalats lemma

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES MODEL-REFERENCE ADAPTIVE SYSTEM (MRAS) MRAS using Lyapunov theory

  • ADAPTIVE SCHEMES GAIN SCHEDULING

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    GS can be regarded as a mapping from processparameters to controller parameters.

    GS can be implemented as a function or a table lookup.

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    It was originally used to accomodate changes in processgain only

    It has a linear controller whose parameters are changedas a function of operating conditions in a programmed wayas a function of operating conditions in a programmed way

    GS based on measurements of operating conditions ofthe process is often a good way to compansate for:

    variations in process parameters or known nonlinearities of the process

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    The main problem is to find suitable scheduling variables

    This is normaly done on the basis of knowledge of thephysics of a system

    Ideally, there should be simple expressions for how thecontroller parameters relate to the scheduling variables

    In process control the production rate can often bechosen as a scheduling variable, since time constants andtime delays are often inversely proportional to productionrate

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    When scheduling variables have been determined, thecontroller parameters are calculated at a number ofoperating conditions by using some suitable design method

    The contoller is thus tuned or calibrated for each The contoller is thus tuned or calibrated for eachoperating condition

    Stability and performance of the system are typicallyevaluated by simulation; particular attention is given to thetransition between different operating points

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Some ideas:

    Linearization of nonlinear actuators Gain scheduling based on measurements ofauxilary variablesauxilary variables Time scaling based on production rate

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Linearization of nonlinear actuator

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Linearization of nonlinear actuator

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Linearization of nonlinear actuator

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    GS based on measurement of auxiliary variables

    TANK IN WHICH THE CROSS SECTION A VARIESWITH HEIGHT h

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    GS based on measurement of auxiliary variables

    TANK IN WHICH THE CROSS SECTION A VARIESWITH HEIGHT h

    22 2

    )()(

    ++=

    sssT

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Time scaling based on production rate

    CONCENTRATION CONTROL

    q(t) = const

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Time scaling based on production rate

    CONCENTRATION CONTROL

    q(t) = const

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Time scaling based on production rate

    CONCENTRATION CONTROL

  • ADAPTIVE SCHEMES GAIN SCHEDULING

    Time scaling based on production rate

    CONCENTRATION CONTROL

    q(t) = const


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